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Popular >

integral from 0 to 1 of x^2-1

Solution

\int_{0}^{1} x^{2} - 1 d x

Solution

- \frac{2}{3}

+1

Decimal Notation

- 0.66666 \dots

Solution steps

\int_{0}^{1} x^{2} - 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{1} x^{2} d x - \int_{0}^{1} 1 d x

\int_{0}^{1} x^{2} d x = \frac{1}{3}

\int_{0}^{1} 1 d x = 1

= \frac{1}{3} - 1

Simplify

\frac{1}{3} - 1 : - \frac{2}{3}

= - \frac{2}{3}

Popular Examples

integral of (3x^4+x^5)

\int (3 x^{4} + x^{5}) d x

(1+y^2)dx+xydy=0

(1 + y^{2}) d x + x y d y = 0

area x= 7/y ,x= y/9 ,x=9y area

x = \frac{7}{y}, x = \frac{y}{9}, x = 9 y

limit as x approaches 0 of 2xcot(x)

x \to 0 lim (2 x cot (x))

derivative of ((2x+x^2)/((1+x)^2))

\frac{d}{d x} (\frac{( 2 x + x ^{2} )}{( 1 + x ) ^{2}})

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of x^2-1 ?
The integral from 0 to 1 of x^2-1 is -2/3